Constantinos Skiadas

Schroder, Mark and Constantinos Skiadas. 2003. Optimal Lifetime Consumption-Portfolio Strategies under Trading Constraints and Generalized Recursive Preferences. Stochastic Processes and Their Applications. 108: 155-505.

We consider the lifetime consumption-portfolio problem in a competitive securities market with essentially arbitrary continuous price dynamics, and convex trading constraints (e.g., incomplete markets and short-sale constraints). Abstract first-order conditions of optimality are derived, based on a preference-independent notion of constrained state pricing. For homothetic generalized recursive utility, we derive closed-form solutions for the optimal consumption and trading strategy in terms of the solution to a single constrained BSDE. Incomplete market solutions are related to complete markets solutions with modified risk aversion towards non-marketed risk. Methodologically, we develop the utility gradient approach, but for the homothetic case we also verify the solution using the dynamic programming approach, without having to assume a Markovian structure. Finally, we present a class of parametric examples in which the BSDE characterizing the solution reduces to a system of Riccati equations.

Schroder, Mark and Constantinos Skiadas. 2002. An Isomorphism between Asset Pricing Models with and without Linear Habit Formation. Review of Financial Studies. 15(4): 1189-1221.

We show an isomorphism between optimal portfolio selection or competitive equilibrium models with utilities incorporating linear habit formation, and corresponding models without habit formation. The isomorphism is expressed through an explicit transformation of consumption plans, utilities, endowments, state prices, wealth processes, security prices, and trading strategies that can be used to mechanically transform known solutions not involving habit formation to corresponding solutions with habit formation. For example, the Constantinides (1990) and Ingersoll (1992) solutions are mechanically obtained from the familiar Merton solutions for the additive utility case, without recourse to a Bellman equation or first order conditions. More generally, recent solutions to portfolio selection problems with recursive utility and a stochastic investment opportunity set are readily transformed to novel solutions of corresponding problems with utility that combines recursivity with habit formation. Our methodology also applies in the context of Hindy-Huang-Kreps preferences, where our isomorphism shows that the solution obtained by Hindy and Huang (1993) can be mechanically transformed to Dybvig's (1995) solution to the optimal consumption-investment problem with consumption ratcheting.

Schroder, Mark and Constantinos Skiadas. 1999. Optimal Consumption and Portfolio Selection with Stochastic Differential Utility. Journal of Economic Theory. 89(1): 68-126.

This paper develops the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuous-time version of recursive utility due to Duffie and Epstein (1992a). The setting is that of a general stochastic investment opportunity set with Brownian information (making some of the results novel in the time-additive case, as well). We characterize the first order conditions of optimality as a system of forward-backward SDE's, and for the Markovian case we show how to solve this system in terms of a system of quasilinear parabolic PDE's and forward only SDE's, which is amenable to numerical computation. Another contribution is a proof of existence, uniqueness, and basic properties for a parametric class of homothetic SDU that can be thought of as a continuous-time version of the CES Kreps-Porteus utilities studied by Epstein and Zin (1989). For this class, we show that the solution method simplifies significantly, resulting in closed form solutions in terms of a single backward SDE (without imposing a Markovian structure). The latter can be easily computed, as we will illustrate with a number of tractable concrete examples involving the type of ``affine'' state price dynamics that are familiar from the term structure literature.

DeMarzo, Peter and Constantinos Skiadas. 1999. On the Uniqueness of Fully Informative Rational Expectations Equilibria. Economic Theory. 13(1): 1-24.

This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as rn-REE. Examples of quasi-complete economies include the type of economies for which demand aggregation in the sense of Gorman is possible (with or without asymmetric information), the setting of the Milgrom and Stokey no-trade theorem, an economy giving rise to the CAPM with asymmetric information but no normality assumptions, the simple exponential-normal model of Grossman (1976), and a case of no aggregate endowment risk. In the common-knowledge context, we provide necessary and sufficient conditions for a common knowledge posterior estimate, given common priors, to coincide with the full communication posterior estimate.

DeMarzo, Peter and Constantinos Skiadas. 1998. Aggregation, Determinacy, and Informational Efficiency for a Class of Economies with Asymmetric Information. Journal of Economic Theory. 80(1): 123-152.

In this paper we identify and analyze a class of economies with asymmetric information that we call quasi-complete. Quasi-complete economies have many of the properties commonly associated with complete markets, but unlike the latter they may support equilibria that do not perfectly aggregate agents' private information. Special cases include a class of economies with traded endowments and linear risk tolerance, Grossman's (1976) exponential-normal model, the setting of the no-trade theorem of Milgrom and Stokey (1982), and an economy with no aggregate endowment risk. For quasi-complete economies we determine equilibrium trades, we show that the set of fully informative equilibria is a singleton, and we give necessary and sufficient conditions for the existence of partially informative equilibria. Besides unifying some familiar settings, the following new results are proved: (a) The same restrictions that deliver Gorman aggregation under symmetric information, are sufficient for Gorman aggregation under asymmetric information, even under partially revealing prices. (b) The traditional assumptions of quadratic utilities and endowment spanning that result in the CAPM under symmetric information deliver a conditional CAPM under asymmetric information, prices that need not be fully informative, and no distributional assumptions. (c) The linear equilibrium in Grossman's (1976) model is the only equilibrium (linear or not), while minor changes in the normality assumptions result in indeterminacy and partially informative equilibria. (d) If there is no aggregate endowment risk, agents with common priors will always sell the risky part of their endowment, no matter what private information they receive.

Skiadas, Constantinos. 1997. Subjective Probability under Additive Aggregation of Conditional Preferences. Journal of Economic Theory. 76(2): 242-271.

This paper provides an axiomatic basis for a representation of personal preferences in which the utility of an act can be expressed as an expected value of conditional utilities of the act given any set of mutually exclusive and exhaustive scenarios, under a unique subjective probability. The representation is general enough to incorporate state-dependent utilities and/or utilities with dependencies across states, as, for example, in the case of disappointment aversion. More generally, this is a model incorporating subjective probability and subjective consequences, since neither probabilities nor consequences are included among its primitives. The model reduces to subjective expected utility under the additional assumptions of separability and state-independence with respect to an objective state-contingent structure of acts.

Skiadas, Constantinos. 1997. Conditioning and Aggregation of Preferences. Econometrica. 65(2): 347-367.

This paper develops a general framework for modeling choice under uncertainty that extends subjective expected utility to include non-separabilities, state-dependence, and the effect of subjective or ill-defined consequences. This is accomplished by not including consequences among the formal primitives. Instead, the effect of consequences is modeled indirectly, through conditional preferences over acts. The main results concern the aggregation of conditional utilities to form an unconditional utility, including the case of additive aggregation. Applications, obtained by further specifying the structure of acts and conditional preferences, include disappointment, regret, and the subjective value of information.